How to I translate an edge in edit mode precisely using numbers?
To Translate any selected Vertices, objects or edges you press G and then after that depending on what axis you want to move it on you press the corresponding letter, which can be Y,X, or Z. 

Secondly, you can either move it yourself with your mouse or type in a number. You can use numbers with decimals and or negative numbers which will translate in the opposite direction. 

As for getting the edge to where you want it to be you will have to experiment with numbers. Hope this helps, and good luck.